How about Winter Sonata? I watched this years ago, so I'm not sure how well it holds up to our modern watching sensibilities (if I remember rightly, the pacing is glacial, a true slow burn) but I loved it at the time.The two main characters fell in love as teenagers and then have to unpack their connection as adults with amnesia, hidden identities, and questionable family histories as stumbling blocks - the heroine thought the hero had died, so "bittersweet" is an understatement! Probably my favourite of the melo classics.

Also If We Were a Season, the drama special. My god, is this wistful. I'm not spoiling a single thing, so if you haven't seen it, go watch it immediately!

Also close-ish to the prompt are: 49 Days, A Werewolf Boy, Baek-hee Has Returned, Do You Like Brahms, Hot Blooded Youth, Missing You (not that I recommend that one), the Japanese manga/anime/film Orange (actually the closest, but obviously not Korean if that's a dealbreaker), and The Classic.

The Third Charm
Our Beloved Summer
Go Back Couple
20th Century Boy and Girl

For a Saguek?
The Moon Embracing the Sun

There will be a Netflix Movie this Friday :p

Otherwise :
- Girls Generation 1979
- Adolescence Medley
- Dance Sport Girls (this one is more realistic than cute but it was really good)

Japanese movies/drama :
- Orange : it has the end I want for Seasons of Blossom
- Your Lie in April
- I Want to Eat Your Pancreas
- Love Relationship
- Enoshima Prism

At Eighteen (A Moment at Eighteen), a drama like a Beatles' song: sweet and thoughtful.

I can think of a lot more Japanese films that fit this than I can Kdramas I've watched. Your Name and (by the same director) Weathering with You have elements of this, but I think the one that fits most closely is From Up on Poppy Hill, which is an inherently wistful movie about two teens grappling with the past as they fall in love.

I don’t think there has been another series like Seasons of blossom because all the other dramas have bullying, or politics in the adult world so that first love element is not able to shine as it has in this show.
I would add Racket boys as my contribution as there is a love story in amongst the found family amongst the two teams staying at the coaches house.